This proposal is to develop new tools to optimize population drug modeling and individualized therapy. Aim 1 will develop new methods for consistent and efficient parametric population modeling using low -discrepancy Faure integration methods. Aim 2 will develop new methods for determining confidence intervals for nonparametric population analysis using profile likelihood techniques. Aim 3 develops a new approach to stochastic dosage optimization using the latest sampling-based methods in nonlinear filtering and a novel method for solving the Bellman stochastic dynamic programming equations. This work will have a broad impact on population modeling and patient care. Most researchers and clinicians now use parametric (P) methods which are not statistically consistent. Much effort is spent on clinical ananlyses using those flawed methods. The new consistent and efficient P method in Aim 1 will be a major advance that will put maximum likelihood P population modeling on a sound statistical footing. Nonparametric (NP) methods of population analysis are also consistent. They can in addition handle mixture distributions from genetically polymorphic populations, and are suitable for "multiple model" (MM) optimal dosage design. However, computationally intensive bootstrap methods are the only current way to obtain NP confidence intervals. Aim 2 will provide a new, more efficient, route to these intervals. Then both P and NP consistent methods will be available to the health care community. NP population modeling is a tool for optimal MM design of coordinated combination dosage regimens of toxic drugs for treatment of AIDS, cancer, infectious diseases, and transplant patients. This, plus feedback from serum, effect, and toxicity measurements can now be combined into a new and unique paradigm for planning and optimizing the entire process of learning about drug behavior in patients while treating them at the same time. This is Aim 3. Such a tool does not exist at present, to our kowledge. For any planned duration of therapy, one will be able to coordinate both the amounts and timing of the doses, and the number and timing of the measurements. The result will be an active therapeutic strategy which achieves desired target goals with optimal precision, rehearsing many future scenarios in advance (this is new). In all three Aims, the end product will be widely disseminated software with user interfaces for research and clinical use.